Are there signs of recent activity? What's on the other side of the hole (or under the floor)?

If there's recent activity, you're suggestion closes a portal but you'll still have a rodent infestation. I think you may need to consider doing more in the way of pest abatement.

Thanks, I really do appreciate your comment. lol But thank goodness this was not the case.
The other side of the wall is the outside of the house. I will find them and seal that up too.
I decided just hardware cloth and filled in the cracks with "great stuff". Now I just have to rebuild the cabinet floor.
I live in a very old house, and as my DH likes to comment "it's falling apart right on schedule"
:) Laura

I had mouse holes under the sink- little jerks were squeezing in the smallest space where the pipes came in. and also the water line to the fridge- you name it- I went around the house with a can of great stuff like a woman on a mission. found over 20 places- and sealed them ALL up. Then, one day- 3 more mice. They had gotten in from under the trailer, through the oven plug. Pulled out oven, sealed that hole, and problem was solved. We only had to stay there a few months- but I learned that the great stuff really works. just find every nook and cranny you can, especially on the inside. I read that the diameter of a pencil is large enough to fit through. Also, steel wool. they won't chew through it.

Close the holes if you want to but that will have no effect on your rodent problem. The only thing that will do that is a lot of traps where they run next to walls. Use ortho home defense max traps for two months to be sure you have gotten the next generation. That might be 20 or more mice.

I have a inch size space under cabinets . What is the best wat to close this space